I'm arriving at Heathrow at 2pm and flying out of Gatwick at 9 am the next morning.
Recommendations on a hostel or inexpensive place to spend the night?
Yotel
You pay by the hour....one idea is to take the tube into London from Heathrow, have some fun in London for a few hours, then take the train down to Gatwick.
The Yotel is in one of the terminals. I've never stayed there but I've heard it's not bad and very convenient.
Right, there's a Yotel at both Gatwick & Heathrow airports. Reserve online at yotel.com.
There's a 4 hour minimum. As an example, a standard room for 8 hours is £58.